I have a character whose death causes the inciting incident of the book. I want to make it clear she is very close to my protagonist in the first few chapters that she's in and perhaps try to make her likable to most readers. Does anyone have any recommendations to making sure this character is well liked and close to the main character in a short time?
I think one of the most important things is to make sure that they are involved with the protagonist's goals or motives. Keep them proactive. It doesn't even have to be anything big. Maybe have them conspiring something with your main character, helping them out with something, showing genuine interest in the protagonist's goals. A good way to score instant points is to show them worrying for your MC in some way. If you're worried about making them likable, try to give them an interesting dynamic. Everyone has seen the "bubbly best friend" and the "completely uninvolved and uninterested friend" and so we tend to shift our gaze away from them. Give them an interesting quirk. In the end it won't be that hard to establish character importance.
You could also show her in flashbacks during the story after her death. Make sure you avoid the 'perfect dead person' trope and show that she was flawed, but still likeable. Maybe have her be almost the complete opposite of the MC, personality-wise?
If you want to show that they're close, maybe physical intimacy e.g. hugging, linking arms, holding hands, kissing (if they're friends, on the cheek/head), etc. You could also have them talk about/mention things that happened a long time ago, to show that they've known each other for a long time. Talking about/mentioning things like things they're afraid of or sensitive about, or dreams/goals could indicate trust.
Hope this helped—happy writing!